臺灣博碩士論文加值系統

本論文著重在於利用各種反射器設計共振腔，包含布拉格反射器、光柵反射器、高對比度光柵以及在聲波所使用週期性排列的小共振腔，並比較彼此之間的差別。與直覺的想法不同，共振腔並不一定要反射面完整的包覆整個腔體，即便反射面充滿了孔洞，甚至孔洞的面積超過了一半，利用側面耦合(Side Coupling)仍然可以設計出共振腔。
在電磁波方面，共振腔都是由介電質所組成，因此在通訊波段將能有比金屬更小的損耗，且與傳統的介電質共振腔相比，傳統的介電質共振腔用介電質差異所造成的反射來將能量束縛在介電質腔體，而在本論文利用的是以介電質當作反射器，將能量束縛在空氣。這樣做的好處是能夠避免能量太高在介電質內產生非線性效應或是超過介電質所能負荷能量。因此，本論文設計的共振腔將能容納更高的能量。
而在聲波方面，本論文以巴克球的結構來排列小型共振腔，證明了即便是在週期性不好的情況下，也能實現球型的共振腔。
本論文將從每一種反射器的反射特性及其頻率響應講起，而後設計簡單的一維共振腔，之後將一維反射器繞成一個圓以設計二維圓柱形的共振腔。一維及二維的共振腔若沿著行進方向有波向量的話，便能夠設計成波導，但不在本論文所探討的範圍內。最終將小型共振腔沿著球殼表面排列，將能夠設計三維的共振腔。

In this studies, we focused on designing resonant cavities by various reflectors, including Bragg reflector, grating reflector, high-index-contrast grating and periodic small resonant cavities employed on acoustic cavities. We compare the differences between different reflectors. Different from our intuitive thinking, the reflectors don’t need to cover the entire cavity surface. Even though the surface of reflection is full of holes, sometimes the area of holes is more than half of total area, we can still use the principle of side coupling to design resonant cavities.
In EM wave, resonant cavities are all composed of dielectric, which has smaller loss compared to metal. Compared to traditional dielectric resonant cavities, which use the index difference to confine energy in the dielectric, in this work, we use dielectric as reflectors and confine energy in the air. The benefits of doing so is to prevent the nonlinear effect caused by high energy and prevent the breakdown of dielectric. Hence, the cavities designed in this work can contain higher energy.
In acoustic wave, we use the structure of Buckyball to arrange our small cavities and prove that even the periodicity is not very good, we can still realize spherical resonator.
We’ll start from the characteristics of each reflector and their frequency response, and then design simple one dimensional cavities. Afterwards, we circle the one dimensional reflector to design two dimensional resonant cavity. If there is a k vector component along the traveling direction, then we can design waveguide, however, this is beyond the scope of this work. Finally we arrange the small cavities along the surface of spherical shell, we can design three dimensional resonant cavities.

口試委員會審定書.........................................#
誌謝....................................................I
中文摘要................................................II
ABSTRACT..............................................III
目錄...................................................IV
圖目錄.................................................VI
表目錄.................................................IX
第一章 簡介............................................1
1.1 文獻回顧.................................1
1.1.1 繞射理論與光柵研究................1
1.1.2 布拉格反射器.....................2
1.1.3 光柵反射器.......................3
1.1.4 高對比度光柵.....................4
1.1.5 共振腔..........................5
1.2 研究動機.................................6
第二章 基本原理.........................................7
2.1 光柵反射器設計原理........................7
2.2 布拉格反射器設計原理.....................11
2.3 聲波設計原理............................12
2.4 共振腔設計原理..........................13
2.5 品質因子................................14
第三章 以布拉格反射器設計共振腔..........................15
3.1 COMSOL Multiphysics模擬軟體介紹.........15
3.2 電磁波布拉格反射器模擬...................16
3.2.1 一維共振腔模擬..................17
3.2.2 二維共振腔模擬..................17
3.3 聲波布拉格反射器模擬.....................19
3.3.1 一維共振腔模擬..................20
3.3.2 二維共振腔模擬..................21
3.3.3 三維共振腔模擬..................22
第四章 以光柵反射器設計共振腔...........................24
4.1 電磁波光柵反射器模擬.....................24
4.1.1 一維共振腔模擬..................27
4.1.2 二維共振腔模擬..................29
4.2 聲波光柵反射器模擬.......................35
4.2.1 一維共振腔模擬..................40
4.2.2 二維共振腔模擬..................41
4.2.3 三維共振腔模擬..................43
第五章 以空氣為介質設計共振腔...........................52
5.1 聲波共振腔..............................52
5.2 聲波共振腔的週期排列.....................55
5.3 以小共振腔排列設計大共振腔................60
5.3.1 一維共振腔模擬..................60
5.3.2 二維共振腔模擬..................61
5.3.3 三維共振腔模擬..................62
第六章 實驗...........................................64
6.1 小型共振腔實驗..........................64
6.2 與模擬結果相比較.........................67
第七章 結論...........................................69
REFERENCE.............................................70

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